Logistic Quantile Regression for Bounded Outcomes Using a Family of Heavy-Tailed Distributions

Abstract

Mean regression model could be inadequate if the probability distribution of the observed responses is not symmetric. Under such situation, the quantile regression turns to be a more robust alternative for accommodating outliers and misspecification of the error distribution, since it characterizes the entire conditional distribution of the outcome variable. This paper proposes a robust logistic quantile regression model by using a logit link function along the EM-based algorithm for maximum likelihood estimation of the p th quantile regression parameters in Galarza (Stat 6, 1, 2017). The aforementioned quantile regression (QR) model is built on a generalized class of skewed distributions which consists of skewed versions of normal, Student’s t, Laplace, contaminated normal, slash, among other heavy-tailed distributions. We evaluate the performance of our proposal to accommodate bounded responses by investigating a synthetic dataset where we consider a full model including categorical and continuous covariates as well as several of its sub-models. For the full model, we compare our proposal with a non-parametric alternative from the so-called quantreg R package. The algorithm is implemented in the R package lqr, providing full estimation and inference for the parameters, automatic selection of best model, as well as simulation of envelope plots which are useful for assessing the goodness-of-fit.